The 3-qubit error-correction quantum circuit is realized and optimized in the non-measuring condition.The modular thought is presented to design and optimize the quantum error-correction circuit. With the quantum bits increasing,the error-correction circuit of 3-qubits can be used in the error-correction circuit of 5-qubits as a module.The error-correction circuit of 5-qubits can be used in the error-correction circuit of 7-qubits.By parity of reasoning,the error-correction circuit of a few quantum bits can be used in the error-correction circuit of multiple quantum bits.The quantum error-correction circuit can be simplified and the redundant qubits can be reduced using the method.It can also make the quantum cost lower.
The 3-qubit error-correction quantum circuit is realized and optimized in the non-measuring condition.The modular thought is presented to design and optimize the quantum error-correction circuit. With the quantum bits increasing,the error-correction circuit of 3-qubits can be used in the error-correction circuit of 5-qubits as a module.The error-correction circuit of 5-qubits can be used in the error-correction circuit of 7-qubits.By parity of reasoning,the error-correction circuit of a few quantum bits can be used in the error-correction circuit of multiple quantum bits.The quantum error-correction circuit can be simplified and the redundant qubits can be reduced using the method.It can also make the quantum cost lower.
Abstract Quantum systems are inherently prone to errors caused by decoherence, noise, and imperfect gate operations. Effective error correction is essential to preserving quantum information, especially under hardware constraints. In this paper, we present a resource-efficient 4-qubit quantum circuit designed to detect and correct single-qubit bit-flip errors within a 3-qubit data block. The circuit uses Feynman (CNOT) and NOT gates alongside an ancillary qubit to implement full correction logic with minimal overhead. Compared to well-known approaches like the 9-qubit Shor code, our design achieves equivalent fidelity (100%) using fewer qubits, making it highly suitable for near-term quantum devices. Simulation results, obtained using IBM Quantum Composer and Qiskit, confirm the circuit’s correctness and reliability across all bit-flip scenarios. The design also introduces a reusable unitary block for efficient implementation. This work offers a scalable and practical solution to quantum error correction using minimal hardware resources.
This paper explores a novel approach to quantum error correction (QEC) centered around the deliberate incorporation of entanglement-based redundancy directly within the design of quantum circuits. Current QEC strategies often rely on external, post-processing correction stages, which introduce significant overhead and complexity. We argue that a more efficient and intrinsically robust solution lies in building self-correcting circuits where redundancy is woven into the circuit's architecture itself, utilizing entangled qubits to detect and mitigate errors in real-time. This approach shifts the paradigm from correction *after* computation to correction *during* computation. The core mechanism involves encoding logical information across multiple physical qubits through carefully designed entangled states, creating a network capable of detecting errors via measurement and then implementing corrective operations through controlled interactions. We present a theoretical framework for designing such circuits, detailing the key considerations for state preparation, entanglement distribution, and error detection/correction protocols. We demonstrate, through mathematical analysis and circuit design principles, that this entanglement-based redundancy can substantially improve the resilience of quantum computations against various noise sources. The proposed method offers a potentially transformative pathway towards fault-tolerant quantum computing, reducing the overall complexity and resource requirements associated with error correction.
In this paper, we discuss the concepts of quantum coding and error correction for a five-particle entangled state. Error correction can correct bit-reverse or phase-flip errors of one and two quantum states and is no longer limited to only one quantum state. We encode a single quantum state into a five-particle entangled state before being transferred to the sender. We designed an automatic error-correction circuit to correct errors caused by noise. We also simplify the design process for a multiple quantum error-correction circuit. We compare error-correction schemes for five and three entangled particles in terms of efficiency and capabilities. The results show that error-correction efficiency and fidelity are improved.
Today's rapid progress in the physical implementation of quantum computers demands scalable synthesis methods to map practical logic designs to quantum architectures. There exist many quantum algorithms which use classical functions with superposition of states. Motivated by recent trends, in this paper, we show the design of quantum circuit to perform modular exponentiation functions using two different approaches. In the design phase, first we generate quantum circuit from a verilog implementation of exponentiation functions using synthesis tools and then apply two different Quantum Error Correction techniques. Finally the circuit is further optimized using the Linear Nearest Neighbor (LNN) Property. We demonstrate the effectiveness of our approach by generating a set of networks for the reversible modular exponentiation function for a set of input values. At the end of the work, we have summarized the obtained results, where a cost analysis over our developed approaches has been made. Experimental results show that depending on the choice of different QECC methods the performance figures can vary by up to 11%, 10%, 8% in T-count, number of qubits, number of gates respectively.
In this work, the efficient quantum error-correction protocol against the general independent noise is constructed with the three-qubit codes. The rules of concatenation are summarized according to the error-correcting capability of the codes. The codes not only play the role of correcting errors, but the role of polarizing the effective channel. For any independent noise, the most suitable error-correction protocol can be constructed based on the rules of concatenation. The most significant aspect of using the concatenated three-qubit codes is to realize quantum error-correction with the non-ideal gate operations, because the error-correction schemes of the three-qubit codes are simple and modular. For example, for the amplitude damping noise with the initial channel fidelity 0.9, the effective channel fidelity can reach 0.94731 (or 0.961634 with the ideal quantum gate operations) when using the 4 levels concatenated quantum error-correction with the three-qubit codes. The protocol with the three-qubit codes needs 81 qubits and 366 quantum gate operations when the accuracy rate is 0.9995. Meanwhile, when using the 3 levels concatenated quantum error-correction with the five-qubit code, the effective channel fidelity can only reach 0.922798 (or 0.975488 with the ideal quantum gate operations). The protocol with the five-qubit code needs 125 qubits and 1147 quantum gate operations when the accuracy rate is 0.9995. The physical resources costed is multiple of the physical resources costed by realizing the three-qubit quantum error-correction, the protocol has a higher fault tolerance threshold, and no increase in complexity. So, we believe it will be helpful for realizing quantum error-correction in the physical system.
While the communication between two sites in the quantum network is carried out,the data frames should be resent once the bit-reversed errors appear.Although this method can guarantee the accuracy of data,the pressure of channel is increased and the communication efficiency is reduced.In order to relieve the pressure of channel,the present quantum bit-reversed error correction circuits were analyzed and improved based on the replication of entanglement and the teleportation to design the seven-particle entanglement of quantum bit-reversed error correction circuits.This improvement can not correct more than three bit-reversed quantum states or phase flip error.The efficiency of protocol and utilization of channels before and after the improvement were compared,and the results show that the latter has higher data transmission utilization and it can supply reference evidence for multi-particle error correction.